We have been developing TwoBody.jl, open-source software for calculating the eigenvalues of the Hamiltonian in quantum mechanical two-body problems. This package serves as a platform for prototyping new methods. It currently includes the Rayleigh-Ritz method and the finite difference method, with plans to incorporate lower bound estimation. In this talk, we demonstrate a workflow for lower bound estimation using both Weinstein’s theorem and Temple’s theorem, which have been applied in quantum chemistry. We welcome feedback from the audience, particularly regarding the mathematical verification of this workflow.